On mod p modular representations which are defined over \F_p

Abstract

In this paper, we use techniques of Conrey, Farmer and Wallace to find spaces of modular forms $S_k({\Gamma }_0(N))$ where all of the eigenspaces have Hecke eigenvalues defined over $\F_p$, and give a heuristic indicating that these are all such spaces.

This is the final version, accepted and to appear in Glasnik Matematicki